Geometry: Logic
Truth Tables!
Do Now:
• What is the converse, inverse, and
contrapositive of the following conditional
statement.
If I am sleepy, then I will yawn a lot.
Truth Tables
• A statement is a sentence that is either true or
false.
– These statements are like the parts of conditional
statements we looked at yesterday (i.e. p/q)
• The truth value of a statement is either true
(T) or False (F).
True or False?
• A rectangle is a quadrilateral
• It is raining outside
• Supplementary Angles add to 90 degrees.
Compound Statement
• Two or more statements joined by the word
and or or.
– So Two Types! AND or OR
Conjunction
A Conjunction is a compound statement with and
Symbol: p^q
Ex: Ms. Stonebraker teaches geometry and algebra.
Example
• Use the following statements to write a compound
statement for each conjunction. Then find the truth
value.
p: The figure is a triangle
q: The figure has two congruent sides
r: The figure has three acute angles
So….. p^r =
So… q^~𝑟
Truth Tables
• A convenient method for organizing truth
values of statements.
Truth Value for Conjunction
p
q
T
T
T
F
F
T
F
F
p^q
Disjunction
• A compound statement that uses the word or
Ex: Billy studies geometry or chemistry.
Symbol: p V q
Example
•
Use the following statements to write a compound statement for each
disjunction. Then find its truth value.
p: January is a fall month
q: January has only 30 days
r: January 1 is the first day of a new year.
pVr
pVq
~𝑝 𝑉 𝑟
Truth Value for Disjunction
p
q
T
T
T
F
F
T
F
F
pVq
Venn Diagram
• A disjunction/conjunction can also be
illustrated with a Venn Diagram! Think about
it.
Example
• The Venn Diagram shows the number of
people who can or cannot attend the May or
the June Spanish Club meetings.
June
MAY
5
6
14
Example Two
• The Venn Diagram shows the number of
graduates last year who did or did not attend
their junior or senior prom.
Junior
85
Senior
123
25
37
Practice
• Try some on your own!
• As always if you are confused please call me
over!
Exit Ticket
• The Venn Diagram shows the students who
take geometry and statistics. How many
students took geometry or statistics? How
many took geometry and statistics? What
does the 25 represent?
Geometry
60
Statistics
5
40
25